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Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Several Existence Theorems of Monotone Positive Solutions for Third-Order Multipoint Boundary Value Problems | Hindawi Publishing Corporation Boundary Value Problems Volume 2007 Article ID 17951 9 pages doi 10.1155 2007 17951 Research Article Several Existence Theorems of Monotone Positive Solutions for Third-Order Multipoint Boundary Value Problems Weihua Jiang and Fachao Li Received 3 May 2007 Accepted 12 September 2007 Recommended by Kanishka Perera Using fixed point index theory we obtain several sufficient conditions of existence of at least one positive solution for third-order m-point boundary value problems. Copyright 2007 W. Jiang and F. Li. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. 1. Introduction We are concerned with the existence of positive solutions for the following third-order multipoint boundary value problems Ú t h t f t u t u t 0 a.e.t e 0 1 u 0 u 0 0 m-2 u 1 x iu i i 1 1.1 where 0 1 2 m-2 1 ai 0 i 1 2 . m - 2 0 y m 12ai 1 h t maybe singular at any point of 0 1 and f t u v satisfies Caratheodory condition. Third-order boundary value problem arises in boundary layer theory the study of draining and coating flows. By using the Leray-Schauder continuation theorem the coincidence degree theory Guo-Krasnoselskii fixed point theorem the Leray-Schauder nonlinear alternative theorem and upper and lower solutions method many authors have studied certain boundary value problems for nonlinear third-order ordinary differential equations. We refer the reader to 1-7 and references cited therein. By using the Leray-Schauder nonlinear alternative theorem Zhang et al. 1 studied the existence of at least 2 Boundary Value Problems one nontrivial solution for the following third-order eigenvalue problems u t Af t u u 0 t 1 u 0 u n u 0 0 1.2 where A 0 is a parameter 1 2 n 1 is a constant and f 0 1 X R X R R is continuous. By using Guo-Krasnoselskii fixed point theorem Guo et al. 2 investigated the existence .
